Method and apparatus for effecting fuzzy control tracking servo

ABSTRACT

Fuzzy control is disclosed in the environment of tracking control for a playback head relative to a medium from which signals are played back. Tracking control data is generated as a function of the detected signal level of the played back signal by using fuzzy inference to obtain direction and magnitude values of the control data which then is used to adjust the tracking of the head.

This application is a continuation, of application Ser. No. 07/579,974,filed Sep. 10, 1990, now abandoned.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to a tracking control arrangement and, moreparticularly, to the use of fuzzy inference, or fuzzy reasoning, toachieve highly accurate tracking control.

2. Description of the Prior Art

Tracking control commonly is used when reproducing previously recordedsignals from a record medium wherein the medium or the playbacktransducers (or heads) or both are movable. For example, automatic trackfinding (ATF) is used conventionally in many video tape recorders tomake certain that the playback heads accurately trace the tracks inwhich video signals have been recorded. ATF control is attained byrecording pilot signals whose frequency alternates between referencefrequencies from track to track, whereby the relative magnitudes ofthese pilot signals picked up during a playback operation are comparedto provide an indication of a tracking error. The deviation of the headfrom the track being scanned is related to the magnitude of the pilotsignal picked up from an adjacent track and, of course, the track fromwhich a pilot signal is picked up is readily discriminated by the pilotsignal frequency. While ATF control is advantageous because it achievesautomatic tracking adjustments without the need for user intervention, atypical ATF control circuit is relatively complicated and expensive.

An alternative to ATF control relies upon the signal level, such as anintegrated value, the envelope or the long term average level, of thereproduced signal as an indication of a tracking error. As described in,for example, Japanese Patent Application No. 245507/1988, the transportspeed of the magnetic video tape is controlled in a manner whichmaintains this signal level above a predetermined threshold. Forexample, as shown in FIG. 1 herein, the signal level of the reproducedsignal is a maximum E_(MAX) when the playback head is disposed at thecenter of the track in which the signal is recorded; but the level ofthe reproduced signal E(n) decreases as the head deviates from the trackcenter. Tracking control is achieved automatically by accelerating ordecelerating the magnetic tape in response to the detected signal levelE(n) which, as shown, is related to the tracking error. The deviation ofthe signal level E(n) from the maximum signal level E_(MAX) is obtainedsimply by comparing the level of the reproduced signal E(n) to thepreset maximum level E_(MAX). The resultant error signal K[E_(MAX)-E(n)] is fed back to the tape transport mechanism as a tracking controlsignal to correct for detected tracking errors.

While the foregoing tracking control arrangement is relatively simpleand achieves tracking correction automatically, various disadvantagesarise with respect thereto. For example, the actual maximum signal levelE_(MAX) which can be reproduced from a particular record medium may besubstantially less than the preset value E_(MAX). This frequently occurswhen signals are recorded on a magnetic tape by one video recorder andreproduced by another having different characteristics. When the actualmaximum signal level is less than the preset level E_(MAX), a propertracking condition will not be detected because the error signalK[E_(MAX) -E(n)] will not be reduced to zero even when there is notracking error. Consequently, in an attempt to achieve trackingcorrection, oscillations may be generated.

Another disadvantage is attributed to the assumption in the trackingcontrol arrangement that the error signal K[E_(MAX) -E(n)] is linear.However, as is appreciated from FIG. 1, changes in the signal level E(n)reproduced from the magnetic tape vary in a non-linear manner withtracking errors. Consequently, and because of this non-linearity, thesensitivity of the tracking control arrangement may increase for largetracking errors but may decrease for small tracking errors. As a result,both transient and steady state response characteristics of thistracking control arrangement may be deficient.

OBJECTS AND SUMMARY OF THE INVENTION

Therefore, it is an object of the present invention to provide atracking control arrangement which avoids the aforenoted defects anddisadvantages, is relatively simple, operates with high accuracy and isrelatively inexpensive to implement.

Another object of this invention is to utilize fuzzy inference, or fuzzyreasoning, for tracking control.

A further object of this invention is to provide an improved techniquefor representing membership functions used in fuzzy reasoning such thatthe circuit implementations, and particularly the memory devices neededto store such membership functions, are relatively simple andinexpensive.

An additional object of this invention is to provide an improvedtechnique for representing membership functions with relatively lowresolution (i.e. the membership functions may be represented by arelatively small number of quantized values) for use with fuzzyreasoning.

Various other objects, advantages and features of the present inventionwill become readily apparent from the ensuing detailed description, andthe novel features will be particularly pointed out in the appendedclaims.

In accordance with this invention, the tracking of a playback headrelative to a medium from which signals are played back is controlled bydetecting the signal level of the played back signal, generatingtracking control data as a function of the detected signal level byusing fuzzy inference; and adjusting the tracking of the head inresponse to that tracking control data.

In one embodiment, tracking control data is generated, in part, byproviding a first set of membership functions representing the detectedsignal level, and a second set of membership functions representingprevious tracking adjustments. Changes which are detected in theplayback signal level are used to determine the particular membershipfunction selected from the first set and the value of the precedingtracking adjustment is used to determine the particular membershipfunction selected from the second set. Tracking control is inferred fromthe membership functions which are selected from the first and secondsets. As one example, tracking adjustment is made by accelerating ordecelerating the record medium from which signals are reproduced; and aprevious tracking adjustment corresponds to a previous amount ofacceleration or deceleration.

As a feature of this embodiment, a third set of membership functionsrepresenting the detected signal level is provided; and a membershipfunction is selected from this third set in response to the detectedlevel of the reproduced signal. Specific reasoning rules are used toinfer the magnitude and direction of tracking control in response to themembership functions selected from this third set and from theaforementioned inferred tracking control.

As yet another feature, the center of gravity of the membershipfunctions which are inferred from the reasoning rules is determined andused as an adjustment signal.

As an aspect of the present invention, a set of membership functions isrepresented by identifying data common to plural membership functions inthe set, the identifying data representing a characteristic relationshipbetween a variable (the variable is, for example, a change in thedetected signal level or a previous tracking adjustment or the detectedlevel of the reproduced signal) and the degree to which the variablesatisfies a particular range. In addition, each membership function inthe set is further represented by position data which locates therespective position of each membership function in that set. In agraphical analysis of the membership functions, the position datarepresents coordinates along an abscissa at which the respectivemembership functions in the set begin.

BRIEF DESCRIPTION OF THE DRAWINGS

The following detailed description, given by way of example, will bestbe understood in conjunction with the accompanying drawings in which:

FIG. 1 is a graphical representation of the relationship betweentracking error and reproduced signal level;

FIG. 2 is a block diagram of one embodiment of an application of thepresent invention to a tracking control arrangement for a video taperecorder;

FIG. 3 is a graphical representation of the relationship between theenvelope level of a reproduced signal and the tracking error of the headused to play back that signal;

FIGS. 4 and 5 are graphical representations of membership functions fortracking control data and for signal level changes, and are useful inunderstanding the present invention;

FIG. 6 represents common identifying data used to represent a membershipfunction shown in FIG. 4 or FIG. 5;

FIG. 7 represents position data for locating the respective membershipfunctions illustrated in, for example, FIG. 4;

FIG. 8 represents a table illustrating the resultant tracking controldirection derived by fuzzy inference in accordance with the presentinvention;

FIG. 9 is a graphical representation of the results of the fuzzyinference in accordance with one example of the operation of the presentinvention;

FIG. 10 illustrates a table representing the magnitude of trackingcontrol derived by fuzzy inference in accordance with the presentinvention;

FIG. 11 is a graphical representation of a set of membership functionsfor the level of the reproduced signal;

FIG. 12 is a graphical representation of the membership functions forthe direction of tracking control derived by the present invention;

FIGS. 13 and 14 are graphical diagrams which are useful in explainingthe manner in which fuzzy inference is used to produce a trackingcontrol direction;

FIG. 15 is a graphical representation of the membership function fortracking control derived by fuzzy inference;

FIG. 16 is a flow chart representing the manner in which a controlsignal is produced from the tracking control membership function derivedby fuzzy inference; and

FIGS. 17A-17C are useful in understanding the manner in which the flowchart of FIG. 16 operates.

DETAILED DESCRIPTION OF CERTAIN PREFERRED EMBODIMENTS

Turning now to FIG. 2, there is illustrated a block diagram of a videotape recorder (VTR) in which the tracking control arrangement of thepresent invention finds ready application. The VTR is provided with apair of oppositely spaced apart record/playback heads 2 and 3 mounted ona rotary drum 4 driven by a drum motor 5. The heads rotate so as to scanslant tracks across a magnetic tape 12 deployed about drum 4 andtransported by a capstan 10 that is driven by a capstan motor 9. Forconvenience and simplification, it is assumed that two tracks arescanned across tape 12 for each rotation of drum 4. That is, for properoperation, tape 12 is advanced by an amount substantially equal to twotrack pitches for each full rotation of the drum.

Drum speed is detected by a frequency generator 7 which, typically, iscomprised of a stationary head that picks up signals produced bymagnetic elements that rotate with drum motor 5, thereby producing asignal whose frequency represents the drum speed. Similarly, the speedof capstan motor 9 is represented by a frequency generator 14 which maybe of similar construction and which also produces a signal whosefrequency is a direct measurement of capstan speed and, thus, of tapespeed. The drum speed and tape speed signals are supplied to a controlcircuit 28, to be described.

When heads 2 and 3 are used to reproduce previously recorded signalsfrom tape 12, the reproduced signal S_(RF) is supplied by way of anamplifier 22 to a demodulating circuit 20 and also to an envelopedetector 30. The demodulating circuit functions to demodulate thereproduced signal S_(RF), such as a video signal, and the demodulatedsignal is supplied to a synchronizing signal separator 24. Thisseparator serves to separate the usual horizontal synchronizing signalS_(H) from the demodulated video signal; and the horizontalsynchronizing signal is supplied to control circuit 28. In addition,vertical synchronizing signal separator 25 coupled to separator 24serves to separate the vertical synchronizing signal S_(V) from thedemodulated video signal; and the separated vertical synchronizingsignal S_(V) also is supplied to control circuit 28. The separatedhorizontal and vertical synchronizing signals are used by the controlcircuit for proper timing control, which forms no part of the presentinvention per se.

Envelope detector 30 operates to detect the envelope ENV of the signalS_(RF) reproduced from tape 12. More particularly, it will beappreciated that the envelope of the reproduced signal varies as shownin FIG. 3 as a function of the tracking of heads 2 and 3 relative to thepreviously recorded tracks on tape 12. The envelope detector serves todetect the lower envelope of the reproduced signal S_(RF) ; and thelevel of the envelope ENV is at a minimum when the heads are in properalignment with the tracks being scanned thereby, and is at a maximumwhen the heads experience maximum tracking error. The detected envelopelevel of the reproduced signal is digitized by an analog-to-digital(A/D) converter 32 and supplied to control circuit 28.

The control circuit functions to maintain drum motor 5 and capstan motor9 at their proper predetermined speeds. In addition, the control circuitresponds to the level of the detected envelope ENV to produce a trackingcontrol signal which is supplied by way of a digital-to-analog (D/A)converter 38 and amplifier 40 to capstan motor 9. The control circuitutilizes fuzzy inference, described below, to attain this trackingcontrol operation.

The speed of drum motor 5 is measured by control circuit 28 by countingthe number of reference clock pulses that are generated during oneperiod of the drum speed signal produced by frequency generator 7. Ifthe measured drum speed differs from a desired speed, a suitable controlsignal is produced by the control circuit and fed back to drum motor 5by way of D/A converter 34 and amplifier 36. Similarly, tape speed ismeasured by the control circuit by counting the number of referenceclock pulses that are generated during one period of the tape speedsignal produced by frequency generator 14. Here too, if the measuredtape speed differs from a desired tape speed, a suitable speed controlsignal is produced by the control circuit and fed back to capstan motor9 by D/A converter 38 and amplifier 40. As will be described, thecontrol circuit also produces an accelerating/decelerating signal whichis supplied to the capstan motor as a tracking adjustment signal.

The manner in which the tracking adjustment signal (also referred toherein as tracking control data) is produced now will be described.

FIG. 3 illustrates the envelope of the playback signal detected byenvelope detector 30. It is appreciated that the level of the detectedenvelope ENV is a minimum when heads 2 and 3 are in proper trackingrelation with the tracks on tape 12. As the heads are displaced fromthis position, the level of the detected enveloped ENV increases. Asrepresented by FIG. 3, if the heads are effectively displaced toward apreceding record track, proper tracking relation is restored bydecelerating capstan motor 9 which reduces the tape speed. Conversely,if the heads are effectively displaced toward the following track, theproper tracking relationship is restored by accelerating the capstanmotor and thus increasing the tape speed.

FIG. 3 also illustrates that if capstan motor 9 is in the process ofbeing decelerated and if the level of the detected envelope ENV isdecreasing, a tracking adjustment is being made so as to return theheads to their proper tracking relation. If, however, the level of thedetected envelope ENV is increasing while the capstan motor is beingdecelerated, the heads are being displaced farther from the desiredtrack and the tracking error will increase. Likewise, if the capstanmotor is being accelerated and if the level of the detected envelope ENVis decreasing, the heads are being returned to proper tracking relation.However, if the level of the detected envelope ENV is increasing whilethe capstan motor is being accelerated, the heads are being furtherdisplaced and the tracking error will increase.

In view of the foregoing, the direction in which a tracking adjustmentis to be made may be determined by detecting the acceleration ordeceleration of capstan motor 9 and by detecting changes in the level ofthe envelope ENV. The present invention proceeds by using fuzzyinference to determine the direction and magnitude of the trackingadjustment which is needed.

Let it be assumed that the tracking control data determined by controlcircuit 28 during the nth time interval, or sample, is represented asCX1(n). Accordingly, the previous tracking control data produced by thecontrol circuit during the (n-1)-th time interval is represented asCX1(n-1). The polarity of this tracking control data CX1(n-1) representsacceleration or deceleration, and the magnitude, or value, thereofrepresents the amount of tracking adjustment that had been applied, suchas the amount of acceleration or deceleration imparted to the capstanmotor. As will be described, control circuit 28 generates trackingcontrol data CX1(n) in response to the preceding tracking control dataCX1(n-1) together with other conditions in accordance with specificreasoning rules, as will be described. Included in these otherconditions is a change in the level of the detected envelope ENV fromone time interval, or sampling time, to the next. This change in thelevel of the envelope is referred to herein as a difference value ΔE(n).

The specific reasoning rules under which control circuit 28 operates toinfer the tracking control direction are as follows:

Rule HK1: If the capstan motor 9 is in the process of being accelerated,that is, if the preceding tracking control data is positive(CX1(n-1)>0), and if the level of the detected envelope ENV isincreasing (ΔE(n)>0), then the capstan motor should be decelerated(CX1(n)<0) to return the heads to their proper tracking position.

Rule HK2: If the capstan motor 9 is in the process of being decelerated,(CX1(n-1)<0), and if the level of the detected envelope ENV isincreasing (ΔE(n)>0), then the capstan motor should be accelerated(CX1(n)>0) to return the heads to their proper tracking position.

Rule HK3: If the capstan motor is in the process of being accelerated(CX1(n-1)>0), and the level of the detected envelope ENV is decreasing(ΔE(n)<0), then the capstan motor should continue to be accelerated(CX1(n)>0).

Rule HK4: If the capstan motor is in the process of being decelerated(CX1(n-1)<0), and the level of the detected envelope ENV is decreasing(ΔE(n)<0), then the capstan motor should continue to be decelerated(CX1(n)<0).

It is appreciated that the foregoing rules do not fully consider themagnitude of acceleration or deceleration or the magnitude of the changein the level of the detected envelope ΔE. Accordingly, in the preferredembodiment, rules HK1 through HK4 are extended to be more explicit tosatisfy the following:

When: (a) the magnitude of the acceleration applied to the capstanmotor, as represented by the tracking control data CX1(n-1), is of anintermediate level, the range of acceleration may be represented as PM(referred to as "positive medium" acceleration), and (b) the magnitudeof the change in the level of the envelope ENV, represented by ΔE(n), isof an intermediate level in the negative direction (a "negative medium"range NM), then the heads exhibit a tracking error in the region ABshown in FIG. 3. Consequently, to correct this tracking error, atracking adjustment should be made of intermediate magnitude in thepositive direction, represented as PM. This is represented as Rule H1:

    CX1(n-1)=PM AND ΔE(n)=NM→CX1(n)=PM.

When the magnitude of acceleration represented by the tracking controldata CX1(n-1) is of an intermediate level in the positive direction,represented by PM, and the change in the detected envelope ΔE(n) also isof an intermediate level in the positive direction, then the headsexhibit a tracking error in the region EF shown in FIG. 3. Consequently,to correct this error, a tracking adjustment should be made ofintermediate magnitude in the negative direction, represented as NM.This is represented as Rule H2:

    CX1(n-1)=PM AND ΔE(n)=PM→CX1(n)=NM

When the magnitude of acceleration CX1(n-1) is of a small level in thepositive direction, represented as PS, and the magnitude of the changein the detected envelope ΔE(n) is of a small magnitude in the negativedirection, represented as NS, then the heads exhibit a tracking error inthe region BC shown in FIG. 3. Consequently, to correct this error, atracking adjustment should be made of a small magnitude in the positivedirection, referred to as PS. This is represented as Rule H3:

    CX1(n-1)=PS AND ΔE(n)=NS→CX1(n)=PS

When the magnitude of acceleration CX1(n-1) is of a small level in thepositive direction (PS), and the magnitude of the change in the detectedenvelope ΔE(n) is of a small level in the positive direction (PS), thenheads exhibit a tracking error in the region DE, shown in FIG. 3. Tocorrect this error, a tracking adjustment should be made of smallmagnitude in the negative direction, referred to as NS. This isrepresented as Rule H4:

    CX1(n-1)=PS AND ΔE(n)=PS→CX1(n)=NS

When the magnitude of acceleration CX1(n-1) is substantially zero,referred to as ZR, and the magnitude of the change in the detectedenvelope ΔE(n) is also substantially zero, then the heads exhibit atracking error in the region CD, shown in FIG. 3. It is appreciated thatthis tracking error likewise is substantially zero and little, if any,tracking adjustment need be made. This tracking adjustment is referredto as ZR, and the foregoing is represented as Rule H5:

    CX1(n-1)=ZR AND ΔE(n)=ZR→CX1(n)=ZR

When the magnitude of acceleration CX1(n-1) is of a small level in thenegative direction (NS), and the magnitude of the change in the detectedenvelope ΔE(n) likewise is of a small level in the negative direction,then the heads exhibit a tracking error in the region ED, shown in FIG.3. To correct this error, a tracking adjustment should be made of smallmagnitude in the negative direction, referred to as NS. This isrepresented as Rule H6:

    CX1(n-1)=NS AND ΔE(n)=NS→CX1(n)=NS

When the magnitude of acceleration CX1(n-1) is of a small level in thenegative direction (NS), and the magnitude of the change in the detectedenvelope ΔE(n) is of a small level in the positive direction (PS), thenthe heads exhibit a tracking error in the region CB, shown in FIG. 3.Consequently, to correct this error, a tracking adjustment should bemade of small magnitude in the positive direction, referred to as PS.This is represented as Rule H7:

    CX1(n-1)=NS AND ΔE(n)=PS→CX1(n)=PS

When the magnitude of acceleration CX1(n-1) is of an intermediate levelin the negative direction (NM), and the magnitude of the change in thedetected envelope ΔE(n) likewise is of an intermediate level in thenegative direction, then the heads exhibit a tracking error in theregion FE, shown in FIG. 3. To correct this error, a tracking adjustmentshould be made of intermediate magnitude in the negative direction,referred to as NM. This is represented as Rule H8:

    CX1(n-1)=NM AND ΔE(n)=NM→CX1(n)=NM

Finally, when the magnitude of acceleration CX1(n-1) is of anintermediate level in the negative direction (NM), and the magnitude ofthe change in the detected envelope ΔE(n) is of an intermediate level inthe positive direction (PM), then the heads exhibit a tracking error inthe region BA, shown in FIG. 3. Consequently, to correct this error, atracking adjustment should be made of intermediate magnitude in thepositive direction, referred to as PM. This is represented as Rule H9:

    CX1(n-1)=NM AND ΔE(n)=PM→CX1(n)=PM

In adopting these reasoning Rules H1-H9, it is assumed that capstanmotor 9 advances tape 12 by an amount equal to two track pitches duringeach full rotation of heads 2,3. Should this relation not apply, such aswhen tape 12 is recorded on a video tape recorder which differs from thevideo tape recorder used for reproduction and thus exhibits differentdrum speeds and/or capstan speeds, tracking errors will be detectedresulting in erroneously inferred tracking adjustments. That is, duringa playback operation, the capstan motor may be erroneously acceleratedor decelerated in an attempt to correct tracking errors which are, inactuality, speed errors caused by different drum or capstan speeds. Inthis regard, control circuit 28 additionally functions to integrate thetracking control data CX1(n-1); and the resultant integrated value isused to compensate the capstan speed control signal normally supplied tocapstan motor 9 as a function of detected capstan speed errors. It willbe appreciated that such speed errors are separate and distinct fromtracking errors.

Consistent with the reasoning Rules H1-H9, acceleration or decelerationof the capstan motor, that is, positive or negative trackingadjustments, are made as a function of whether the tracking control dataCX1(n-1) increases or decreases. It may be thought, however, thatcontrol over the capstan motor for tracking error correction may beeffected in accordance with the following equation: ##EQU1## whereA_(i), B_(i) and C are coefficients, CX1(i) is the tracking control dataat the i-th time interval, or sample, CX2(i) is the error signal at thei-th time interval or sample that is the difference between the actualand desired capstan speed and Im(n) is the motor current through thecapstan motor which varies with the torque of that motor. When equation(1) is applied to reasoning Rules H1-H9, A_(i) =A.sub.(n-1) =1 and B_(i)=C=0.

While an implementation of equation (1) possibly may result in inferredtracking control data with higher accuracy, such increase in accuracy ismore than offset by the complexity of the control circuit needed tocarry out the arithmetic operations of this equation (1). It has beenfound that, as a practical matter, the accuracy achieved in inferringtracking control from reasoning Rules H1-H9 is sufficiently high and,moreover, the control circuit may be implemented, both in hardware andin software, in an overall arrangement which is substantiallysimplified.

The manner in which control circuit 28 executes the reasoning RulesH1-H9 now will be described. One of ordinary skill in the art willappreciate that control circuit 28 includes a commercially availablemicroprocessor (the particular manufacturer and model form no part ofthe present invention per se) and, additionally, may include fuzzy logiccircuits of the type described in U.S. Pat. Nos. 4,694,418 and4,837,725. The microprocessor is programmed to carry out theaforementioned reasoning rules (as well as additional reasoning rulesdescribed below) and fuzzy logic implementations, such as described inU.S. Pat. Nos. 4,760,896 and 4,864,490.

Referring now to FIG. 4, there is graphically illustrated a set ofmembership functions which represent the degree to which the trackingcontrol data CX1(n-1) satisfies predetermined ranges. Seven membershipfunctions are illustrated as follows:

PL=positive large

PM=positive medium

PS=positive small

ZR=substantially zero

NS=negative small

NM=negative medium

NL=negative large

The abscissa shown in FIG. 4 represents a normalized variable, in thiscase CX1(n-1). The normalized value 0 corresponds to precise trackingalignment of a head with respect to a data track, the normalized value+1 represents a tracking error corresponding to one full positive pitchwidth and the normalized value -1 represents a tracking errorcorresponding to one full negative pitch width. The ordinate representsthe degree to which the normalized variable satisfies the indicatedrange; and in the illustrated embodiment, the membership functions PM,PS, ZR, NS and NM are substantially triangular in shape. As used herein,the "value" of a membership function means the degree to which thevariable satisfies a respective range. The set of membership functionscorresponding to tracking control data CX1(n-1) may be stored in amemory, such as a ROM, by quantizing each membership function such thateach quantized sample is stored as a digital representation of thesample value and the abscissa location (or coordinate) of that sample.

Similarly, the expected values of changes in the detected envelope ΔE(n)may be represented as the set of membership functions shown graphicallyin FIG. 5. Here too, the set is comprised of membership functions PL,PM, PS, ZR, NS, NM and NL, respectively. After normalization of thevariable ΔE(n) it is appreciated that each membership function includedin the set illustrated in FIG. 5 is substantially similar to themembership functions illustrated in FIG. 4. The set of membershipfunctions for envelope changes ΔE(n) may be digitized and stored in amemory, such as the same memory used to store the membership functionsfor tracking control data CX1(n-1).

Preferably, to represent a set of membership functions, the abscissaextending from -1 to +1 is divided into thirty-two samples. Eachmembership functions in a set thus may be stored as a subset of thesethirty-two samples. For example, since reasoning Rules H1-H9 utilizemembership functions PM, PS, ZR, NS and NM for tracking control dataCX1(n-1), that is, the membership functions PL and NL are not used bythese reasoning rules, then the set of membership functions for CX1(n-1)may be represented as 5×32=160 samples. Likewise, if each membershipfunction included in the set for envelope changes ΔE(n) is quantizedinto thirty-two samples, then, since only five membership functions forΔE(n) are used in reasoning Rules H1-H9 (membership functions PL and NLare not used), 160 samples must be stored. The set of membershipfunctions for tracking control data CX1(n) inferred by reasoning RulesH1-H9 likewise may be stored as 160 samples.

It is appreciated that, when the abscissa of FIGS. 4 and 5 is dividedinto thirty-two samples, the triangular characteristic may berepresented with relatively low resolution by five samples. FIG. 6illustrates these five samples and is referred to as membership functiondata D_(BASE). This membership function data represents thecharacteristic relationship (e.g. triangular) between the variable (suchas CX1(n-1) or ΔE(n) or CX1(n)) and its degree of satisfaction in theparticular range (such as the range PM, PS, ZR, NS or NM). The remainingtwenty-seven samples for each membership function are essentially zero.It is recognized that such zero-value samples are redundant and, ifstored, unnecessarily occupy useful memory space. It is a feature of thepresent invention to minimize the memory requirements for storing thesets of membership functions.

Since the membership function data D_(BASE) shown in FIG. 6 issubstantially the same for each membership function in each set, thismembership function data may be stored as common data D_(BASE) and usedto represent each memory function. Thus, rather than storing fifteenduplicate membership function data, only one D_(BASE) need be stored. Inaddition, position data, referred to as D_(SUB), may be stored torepresent the beginning location of each membership function along theabscissa. Thus, and as shown in FIG. 7, for tracking control dataCX1(n-1) the membership function PM begins at sample 21 along theabscissa, membership function PS begins at sample 17, membershipfunction ZR begins at sample 13, membership function NS begins at sample9 and membership function NM begins at sample 5. Consequently, ratherthan representing each membership function with thirty-two samples, onlysix samples need be used: five samples representing the membershipfunction data D_(BASE) shown in FIG. 6 and one sample representing theposition data D_(SUB) which identifies the coordinate along the abscissaat which the membership function begins.

Since membership functions PM, PS, ZR, NS and NM in each set exhibitsubstantially the same characteristic relationship, common membershipfunction data D_(BASE) is used to represent all of the membershipfunctions, and each membership function additionally is represented by aunique position data D_(SUB). While the fifteen membership functions maybe represented by the five samples comprising common membership functiondata D_(BASE) and fifteen samples representing the position data foreach membership function, the fifteen position data samples needed forall sets may be reduced further to only five samples if a particularmembership function in one set is located at the same position along theabscissa as that membership function in the other set. For example, theposition data for membership function NM of the set for tracking controldata CX1(n-1) may be equal to the position data for the membershipfunction NM of the set for envelope change ΔE(n). Optimally, one set ofsamples representing the triangular characteristic relationship of amembership function and five samples representing the position data foreach membership function may be used in common for the tracking controldata CX1(n-1), the envelope change ΔE(n) and the tracking adjustment, oracceleration CX1(n).

In accordance with the foregoing, a memory of relatively small capacitymay be utilized effectively to store a table which represents therespective sets of membership functions.

Although not utilized by reasoning Rules H1-H9, nevertheless themembership functions PL and NL for each set are stored. These membershipfunctions are used by other reasoning rules, to be described, forinferring the magnitude of the tracking control signal to be applied tothe capstan motor. Stated more broadly, these membership functions PLand NL are used to infer the magnitude of the tracking adjustment neededto correct tracking errors.

FIG. 8 illustrates a table for inferring tracking control directionCX1(n) for the different membership functions that may be exhibited bytracking control data CX1(n-1) and envelope changes ΔE(n) in accordancewith reasoning Rules H1-H9. It is appreciated that the reasoning rulesexclude certain conditions, such as when CX1(n-1)=NM and ΔE(n)=NS, ZR orPS. Such conditions either cannot occur or are highly unlikely and, ifthey do in fact occur, the remaining reasoning rules are sufficient toaccommodate such conditions. For example, if CX1(n-1)=NM and ΔE(n)=NS,then the reasoning rule for CX1(n-1)=NM and ΔE(n)=NM plus the reasoningrule for CX1(n-1)=NS and ΔE(n)=NS are used to infer the proper trackingcontrol direction CX1(n). By limiting the fuzzy inference operation toreasoning Rules H1-H9, the overall arithmetic operation andimplementation thereof is greatly simplified.

Control circuit 28 is adapted to infer the tracking control direction byusing the "Mamdani" technique. (Examples of this are described in, interalia, "Process Control Using Fuzzy Logic" Mamdani et al Fuzzy SetsTheory and Applications to Policy Analysis and Information Systems, NewYork: Plenum, 1989, pages 249-265 and "An Experiment in LinguisticSynthesis with a Fuzzy Logic Controller" Mamdani et al , InternationalJournal Man-Machine Studies, Vol. 7, pages 1-13, 1973). Accordingly, thecontrol circuit normalizes the tracking control data CX1(n-1) derived atthe preceding time interval, or sampling time, and also normalizes theenvelope change ΔE(n) detected at the present sampling time; and thesenormalized variables CX1(n-1) and ΔE(n) are used to read from the memorythose membership functions for CX1(n-1) and ΔE(n) which are satisfied bythese normalized variables. Then, the selected membership functionswhich are read from the memory are further processed to infer a trackingcontrol direction value. The manner in which membership functions areselected from the memory and then processed will best be appreciated bya numerical example.

Let it be assumed that the tracking control data CX1(n-1) derived duringthe preceding sample is such that, when normalized, it exhibits a valueof 0.45. With reference to FIG. 4, this normalized variable has thevalue 0.7 in membership function PM and the value 0.2 in membershipfunction PS. Let it be further assumed that the presently sampledenvelope level differs from the previous sample by an amount which, whennormalized, is equal to -0.4. From FIG. 5, this normalized variable hasthe value 0.6 in membership function NM and the value 0.3 in membershipfunction NS.

Now, in accordance with reasoning Rule H1, and as seen from the tableshown in FIG. 8, since the normalized value of CX1(n-1) satisfiesmembership function PM and since the normalized value of ΔE(n) satisfiesmembership function NM, it is inferred that tracking error data CX1(n)is within membership function PM. Control circuit 28 reads from thememory the membership function and position data which representsmembership function PM for tracking control data CX1(n). That is,membership function data D_(BASE) and position data D_(SUB) are read toprovide a suitable representation of this membership function PM, whichmay be similar to the membership function PM shown in FIG. 4.

In accordance with the Mamdani method, the membership characteristic PMfor tracking control data CX1(n) is limited in its maximum value to thelesser of the membership function values corresponding to normalizedCX1(n-1) and normalized ΔE(n). In the present example, the value of themembership function NM for ΔE(n) is equal to 0.6 and is less than thevalue 0.7 of membership function PM for normalized CX1(n-1).Consequently, the maximum value of the membership function PM for CX1(n)is limited to 0.6. Hence, and as shown in FIG. 9, membership function PMfor the tracking control direction CX1(n) is truncated, or limited, to amaximum value of 0.6. This limited membership function thus appearstrapezoidal in shape.

A similar operation is carried out when applying each of the remainingreasoning rules H2-H9. That is, the membership function for the trackingcontrol direction CX1(n) is inferred from the membership functions forthe preceding tracking control data CX1(n-1) and the present envelopechange ΔE(n), and the maximum value of the inferred membership functionfor the tracking control direction CX1(n) is limited to the smaller ofthe value of the membership function corresponding to the normalizedvariable CX1(n-1) or ΔE(n).

Continuing with the present example, from FIG. 4, it is seen that thenormalized value 0.45 for CX1(n-1) has the membership function value 0.2of membership function PS. From FIG. 5, it is seen that the normalizedvalue 0.4 for ΔE(n) has the membership function value 0.3 of membershipfunction NS. In accordance with reasoning Rule H3, the tracking controldirection CX1(n) is inferred to be within membership function PS. Heretoo, the membership function PS for tracking control direction CX1(n) islimited, or truncated, by the smaller of the value of membershipfunction PS corresponding to the normalized value of CX1(n-1) andmembership function NS corresponding to the normalized value of ΔE(n).In the present example, the value of membership function PScorresponding to the normalized value of CX1(n-1) is equal to 0.2, whichis smaller than the value 0.3 of the membership function NScorresponding to the normalized value of ΔE(n). This smaller valuelimits the magnitude of membership function PS for tracking controldirection CX1(n).

FIG. 9 illustrates the two truncated membership functions PS and PMwhich contain the tracking control direction CX1(n) inferred byreasoning Rules H1 and H3. The illustrated membership functions whichare satisfied by the tracking control direction CX1(n) are subjected toan OR operation, resulting in a membership function characteristicrepresented by the solid line in FIG. 9. As will be described below, atracking control direction value may be derived from the membershipfunction characteristic shown in FIG. 9 by determining the center ofgravity of that characteristic. It is appreciated that the coordinate ofthat center of gravity along the abscissa represents the normalizedtracking control direction value. As will also be described below, thevalue of the tracking control magnitude is inferred from the membershipfunction characteristic derived for tracking control direction CX1(n).That is, the membership function characteristic shown in FIG. 9 is usedto infer the value of the tracking control magnitude.

It will be appreciated that the foregoing discussion has explained howthe value of the direction of tracking control is obtained. The mannerin which control circuit 28 derives a value of the tracking controlmagnitude CX1(n) now will be described.

Control circuit 28 operates in accordance with particular reasoningrules to infer the amount, or magnitude, of tracking control as follows:

Rule RK1: When the signal level E(n) of the detected envelope ENV issmall, the amount of tracking adjustment, or tracking control (CX1(n)),such as the amount of acceleration applied to the capstan motor, issubstantially zero.

Rule RK2: When the signal level E(n) of the envelope is slightly largerand it has been inferred (from the preceding discussion) that thedirection of tracking control is positive (D(n)>0), that is, it has beendetermined that the capstan motor should be accelerated, a small amountof positive tracking control CX1(n) is provided, that is, the capstanmotor is accelerated by a small amount.

Rule RK3: When the signal level E(n) of the envelope is slightly larger,and it has been inferred that tracking control should be applied in thenegative direction (D(n)<0), that is, it is determined that the capstanmotor should be decelerated, then the magnitude of tracking controlCX1(n) is small (i.e. a small amount of deceleration is applied to thecapstan motor).

Rule RK4: When the signal level E(n) of the envelope is of anintermediate (or medium) level, and it has been inferred that thetracking control direction is positive (D(n)>0), that is, the capstanmotor should be accelerated, then the amount of tracking control CX1(n)to be applied is large, that is, a large amount of acceleration isapplied to the capstan motor.

Rule RK5: When the signal level E(n) of the envelope is of anintermediate level and it has been inferred that the tracking controldirection is negative (D(n)<0), that is, it is determined that thecapstan motor should be decelerated, then the magnitude of the trackingcontrol CX1(n) is large, that is, a large amount of deceleration isapplied to the capstan motor.

Rule RK6: When the signal level E(n) of the envelope is large, then themagnitude of the tracking control CX1(n) is large and is applied in thenegative direction, that is, a large amount of deceleration is appliedto the capstan motor.

Representing the signal level E(n) by the same notations that have beenused above to designate substantially zero (ZR), small (PS),intermediate (PM) and large (PL), and representing the positive andnegative directions of tracking control as P and N (which correspond toacceleration and deceleration, respectively), then the foregoingreasoning rules may be summarized as follows:

Rule R1

E(n)=ZR→CX1(n)=ZR

Rule R2

E(n)=PS AND D(n)=P→CX1(n)=PS

Rule R3

E(n)=PS AND D(n)=N→CX1(n)=NS

Rule R4

E(n)=PM AND D(n)=P→CX1(n)=PL

Rule R5

E(n)=PM AND D(n)=N→CX1(n)=NL

Rule R6

E(n)=PL→CX1(n)=NL

Rules R1-R6 are summarized in the table illustrated in FIG. 10. Forconvenience, and to reduce the requisite reasoning rules needed to inferthe magnitude of tracking control to correct for large errors, it isassumed that when the level of the detected envelope E(n) is large, atracking adjustment will be made in the negative direction. That is,CX1(n) is assumed to be a large negative value NL irrespective of theactual direction that may be inferred by the aforementioned Rules H1-H9.Hence, for large tracking errors, tracking correction is achieved byapplying a large deceleration to the capstan motor.

FIG. 11 is a graphical representation of the membership functions whichmay be satisfied by the envelope level E(n). From FIG. 3, it isappreciated that the envelope always is positive and, thus, membershipfunctions NS, NM and NL are not needed to represent the envelope level.Membership function and position data representing the set of membershipfunctions for the envelope level E(n) are stored in the memory in amanner similar to that by which the membership functions discussed aboveare stored.

FIG. 12 is a graphical representation of the membership functions forthe tracking control direction D(n) inferred by reasoning Rules H1-H9.It is appreciated that the tracking control direction is either positiveP or negative N. Here too, membership function and position datarepresenting these membership function characteristics are stored in thememory.

FIGS. 13 and 14 are graphical representations of the relationshipbetween the inferred tracking control direction as determined byreasoning Rules H1-H9 and the membership functions P and N,respectively, of the tracking control direction. The inferred trackingcontrol direction FD(n) is illustrated for the example discussed abovein conjunction with FIG. 9. The shaded portions in FIGS. 13 and 14designate the overlapped portions between the inferred tracking controldirection FD(n) and the membership functions P and N for the trackingcontrol direction. These shaded portions represent the maximum values ofthe control direction and are applied in reasoning Rules R1-R6 to detectthe front conditions of those rules. These front conditions are used bycontrol circuit 28 to limit the membership functions for trackingcontrol data CX1(n) inferred by Rules R1-R6 and shown in the table ofFIG. 10. That is, these front conditions limit the maximum values ofmembership functions NL, NS, ZR, PS and PL which are inferred byreasoning Rules R1-R6.

In accordance with the present invention, to reduce the amount of dataneeded to represent the membership functions for tracking control dataCX1(n), the membership functions which are stored in the memory fortracking control data CX1(n-1) are used as the membership functions forthe tracking control data CX1(n). In particular, the membershipfunctions NL, NS, ZR, PS and PL for tracking control data CX1(n-1) arethe same membership functions NL, NS, ZR, PS and PL for tracking controldata CX1(n). By reducing the amount of data needed to be stored in thememory, the overall complexity of the control circuit may be reduced.

When selecting a membership function from the memory for CX1(n) asinferred by Rules R1-R6 based upon the detected envelope level E(n) andthe tracking control direction D(n), the maximum value of the selectedmembership function is limited by the lesser of the value of themembership function corresponding to E(n) and the membership functioncorresponding to D(n) in a manner similar to that discussed above inconjunction with FIG. 9. Thus, for reasoning Rule R1, the membershipfunction ZR for tracking control data CX1(n) is limited by the value ofthe membership function ZR corresponding to the envelope signal levelE(n) .

Similarly, for reasoning Rule R2, the maximum value of membershipfunction PS read from the memory for tracking control data CX1(n) islimited by the lesser of the value of the membership function PScorresponding to the detected envelope level E(n) and the value of themembership function P corresponding to the inferred tracking controldirection D(n). A similar limitation in the maximum value of themembership function for tracking control data CX1(n) which is inferredby Rules R3-R6 is effected as a function of the lesser of the value ofthe membership function corresponding to the detected envelope levelE(n) and the value of the membership function corresponding to theinferred tracking control direction D(n). Of course, the membershipfunction NL for tracking control data CX1(n) of Rule R6 is limited bythe value of the membership function PL corresponding to the detectedenvelope level.

FIG. 15 is a graphical representation of the inferred tracking controlmagnitude in accordance with the following example: it is assumed thatD(n)=P and that the detected envelope level E(n) is normalized as Ea,shown in FIG. 11. Accordingly, the envelope level Ea has a correspondingvalue b in membership function PS and a corresponding value a inmembership function ZR. From rule R1, the tracking control data CX1(n)is inferred to be in membership function ZR; and from the Mamdanitechnique, this membership function ZR is limited, or truncated to thevalue a. This limitation in the membership function ZR for CX1(n) isshown in FIG. 15. Likewise, for rule R2, the tracking control dataCX1(n) is inferred to be in membership function PS; and from the Mamdanitechnique, this membership function PS is limited to the value b asshown in FIG. 15. As before, these two membership functions ZR and PSfor tracking control data CX1(n) are subjected to an OR operation,illustrated by the solid line in FIG. 15.

It will be appreciated that, by using fuzzy inference to obtain trackingcontrol data, accurate tracking control is attained even if the signalS_(RF) reproduced from the record medium varies in signal level.Furthermore, even the non-linear changes in the reproduced signal levelhave little affect upon the tracking control derived by the use of fuzzyinference discussed above. Hence, both transient and steady-statetracking control characteristics are improved over the prior art.Although some prior art proposals contemplate the use of simulating theplayback and tracking apparatus with a computer model, the fact that thereproduced signal S_(RF) varies non-linearly makes it difficult toprovide such a simulated model. Whereas the prior art model simulationapproach thus may not provide precise tracking control, errors due tosuch non-linearity in the reproduced signal are avoided by the fuzzyinference technique of the present invention.

The manner in which a tracking control signal is produced from themembership functions of the tracking control data produced by the fuzzyinference technique of the present invention now will be described. Forsimplification, it is assumed that the tracking control data membershipfunction is of the type illustrated in FIG. 15. It will, nevertheless,be appreciated that other membership function characteristics will beinferred for different levels of the reproduced signal envelope and fordifferent changes in that envelope. The processor included in controlcircuit 28 is programmed to carry out the routine shown in FIG. 16 whichfunctions to detect the center of gravity of the membership functioncharacteristic which has been inferred for the tracking control dataCX1(n).

Assuming that the membership function illustrated in FIG. 15 representsthe tracking control data inferred by reasoning Rules H1-H9 and R1-R6,this membership function characteristic is sampled by providing, forexample, thirty-two samples along the abscissa from -1 to +1. The valueof each sample represents the membership function characteristic of thetracking control data CX1(n), and it is appreciated that the maximumvalue of the membership function characteristic at any sampling point isno greater than 1. Each of the thirty-two sampling points may berepresented by a 5-bit address. Accordingly, since membership functionZR (in FIG. 15) begins at sampling point 13 (as discussed above inconjunction with FIG. 7), it is appreciated that, for the first twelvesampling points, or addresses, membership function data equal to 0 isstored.

FIG. 17A illustrates eight sampling points (0-8) of the membershipfunction characteristic shown in FIG. 15. FIG. 17B represents the valueof the membership function characteristic at each sampling point and,for a purpose soon to be explained, each sampling point in FIG. 17A isassociated with a corresponding address (such as address 1, 2, . . . 6 .. . etc.). Referring to the flow chart shown in FIG. 16, the manner inwhich the control circuit carries out the illustrated routine todetermine the center of gravity of the membership functioncharacteristic now will be discussed.

After starting the routine at instruction SP1, the control circuitcumulatively adds the value at each sampling point to the summation ofthe values obtained at the preceding sampling points, as represented byinstruction SP2. FIG. 17C represents the cumulative addition fromsampling point to sampling point, with each cumulative sum being storedat a corresponding address. Thus, the value of the membership functioncharacteristic at sampling point 1 is added to the value of themembership function characteristic at sampling point 0 and is stored inaddress 1 corresponding to sampling point 1. Then, the value of themembership function at sampling point 2 is added to the previousaccumulated sum stored at address 1, and this cumulative sum is storedin address 2 corresponding to sampling point 2. This process repeatsuntil the cumulative sum of the values of the membership functioncharacteristic at all of the sampling points is stored in address 7corresponding to sampling point 7.

The control circuit then advances to instruction SP3 which divides thecumulative sum in address 7 by the factor 2. In the example shown inFIG. 17, the cumulative sum 2.5 is divided by 2, resulting in thequotient 1.25. Then, control circuit 28 advances to instruction SP4 todetermine the address at which the cumulative sum closest to thisquotient (1.25) is stored. From FIG. 17, it is seen that the cumulativesum of 1.1 is stored in address 4, and this is closer to the quotient1.25 than the cumulative sum 1.8 (stored in address 5) or 0.8 (stored inaddress 3). Address 4 is referred to as the "gravity center near data"and represents the address closest to the center of gravity of theillustrated membership function characteristic.

Next, the control circuit advances to instruction SP5 to determine theaddress adjacent address 4 which stores the cumulative sum that is closeto the quotient 1.25. From FIG. 17, it is seen that address 5corresponds to this requirement and is referred to as an "adjacent dataaddress". Then, the center of gravity is detected by interpolating theaddress between addresses 4 and 5 that correspond to the address atwhich the quotient 1.25 would have been stored. This interpolation isobtained in accordance with the following equation:

    (1.25-1.1)/(1.8-1.1)=0.21                                  (2)

The resultant, interpolated value 0.21 is added to address 4 (i.e. it isadded to the "gravity center near data") resulting in a sampling point,or address, at the center of gravity of 4.21. It is this interpolatedcenter of gravity address that is used as the tracking control signal.

It is appreciated that the center of gravity of the membership functioncharacteristic is determined with high accuracy without requiring theuse of a large number of samples to represent the membership functions.That is, high accuracy is achieved with low membership functionresolution. This center of gravity then is normalized and supplied bycontrol circuit 28 to D/A converter 38 for selectively accelerating ordecelerating capstan motor 9 of FIG. 2.

It will be appreciated that instruction SP3 for dividing the cumulativesum by the factor 2 may be achieved simply by shifting the digital valueof the cumulative sum by one bit. That is, this division may be achievedby deleting the least significant bit from the cumulative sum. Hence,the overall arithmetic operation relied upon to derive the trackingcontrol data from the membership function characteristic CX1(n) isrelatively simple, and employs simple division and addition. Locatingthe center of gravity of a function may be defined by the followingequation: ##EQU2## If equation (3) is followed precisely, the overallarithmetic operations needed to implement this equation (assuming theuse of thirty-two samples to represent a membership functioncharacteristic) consists of thirty-two multiplication operations,sixty-four addition operations and one division operation. However, byrelying upon-the routine illustrated in FIG. 16, the center of gravitymay be detected accurately and easily without requiring several repeatedoperations. That is, the routine illustrated in FIG. 16 which detectsthe center of gravity is far simpler than the mathematical routineneeded to implement equation (3).

In actual control over capstan motor 9 (FIG. 2), the tracking controlsignal derived from the center of gravity of the membership functioncharacteristic produced by the fuzzy inference technique discussed aboveis combined with the capstan speed control signal normally produced bythe control circuit; and the combined signal is applied as a capstancontrol signal to the capstan motor. Thus, the capstan is driven at acontrolled, predetermined speed with selective acceleration anddeceleration to provide proper tracking control such that heads 2, 3precisely scan the slant tracks recorded on tape 12.

To summarize the manner in which the present invention provides fuzzytracking control, the envelope ENV of the signal S_(RF) reproduced fromtape 12 by heads 2, 3 is detected in envelope detector 30; and thedetected envelope level is supplied to control circuit 28. Changes ΔE(n)in the envelope are obtained, and these envelope changes ΔE(n) togetherwith the previous tracking control data (or tracking adjustment)CX1(n-1) are subjected to fuzzy inference in accordance with RulesH1-H9. Thus, the tracking control direction is inferred by the reasoningrules. Then, the inferred tracking control direction together with thedetected envelope signal level E(n) are subjected to fuzzy inference inaccordance with reasoning Rules R1-R6 to produce the tracking controlmagnitude value. The resulting tracking control data is expressed as amembership function characteristic whose center of gravity is determinedand, when normalized, is applied to capstan motor 9 to correct fortracking errors. That is, the capstan motor is accelerated ordecelerated in a manner which brings heads 2, 3 into proper alignmentwith the slant tracks recorded on tape 12.

By utilizing fuzzy inference, a correct tracking control operation iseffected even if the level of the signal S_(RF) reproduced from tape 12changes. Moreover, the non-linear relationship between the level of thereproduced signal and the tracking error does not adversely affect thetracking control data produced by the fuzzy inference of the presentinvention. Moreover, the present invention exhibits significantsimplification because the data which must be stored to represent thevarious membership functions discussed above can be minimized, wherebymembership function data D_(BASE) and position data D_(BASE) may be usedto represent all membership functions. This reduces the capacity of thememory needed to store the membership functions and, as a result,simplifies the overall tracking control circuit. Still further, thepresent invention relies upon a relatively simple technique to determinethe center of gravity of the membership function characteristicrepresentative of the tracking control data. This simplifiedimplementation nevertheless produces highly accurate tracking controlwhile minimizing the resolution needed to represent the membershipfunctions.

While the present invention has been particularly shown and describedwith reference to preferred embodiments, it will be readily appreciatedby those of ordinary skill in the art that various changes andmodifications may be made without departing from the spirit and scope ofthe invention. For example, tracking control has been described in thecontext of selectively accelerating or decelerating the capstan motor.Alternatively, tracking control may be achieved by automatic trackfollowing, such as by using the relative amplitudes of recorded pilotsignals as tracking error indications. Furthermore, for purposes ofsimplification, equation (1) above is implemented by settingcoefficients B_(i) and C equal to zero. If desired, equation (1) may beimplemented in its entirety. Still further, although the Mamdaniinference technique is preferred, the present invention is not limitedsolely to that technique. It is appreciated that other methods ofinferring membership function characteristics may be adopted.

It also is noted that, although the present invention has been describedin the environment of a video tape recorder, this invention finds readyapplication to other environments in which tracking control normally iscarried out. For example, tracking control in digital audio tape (DAT)recorders, optical disk devices, hard disk drives, and the like, may beeffected by the present invention.

Still further, although common membership function data D_(BASE) hasbeen described above as being representative of the various membershipfunctions shown in, for example, FIGS. 4, 5 and 11, each set ofmembership functions may be represented by membership function datacommon to that set alone.

It is intended that the appended claims be interpreted as covering thespecific embodiments discussed above, the aforementioned alternativesand applications and all equivalents thereto.

What is claimed is:
 1. A method of controlling a tracking of a headrelative to a medium from which signals are played back comprising asteps of: detecting a signal level of signals which are played back;generating present tracking control direction and magnitude values as afunction of the detected signal level by providing a first set ofmembership functions representing respective degrees to which changes inthe detected signal level satisfy predetermined ranges of change,providing a second set of membership functions representing respectivedegrees to which previous tracking control direction and magnitudeadjustments satisfy predetermined ranges of adjustment, determiningparticular membership functions from said first and second setscorresponding to a detected signal level change and to a precedingtracking control direction and magnitude adjustment, and inferring saidpresent tracking control direction and magnitude values from thedetermined membership functions; and adjusting the tracking of said headin response to the present tracking control value.
 2. The method ofclaim 1 wherein at least one of the steps of providing a set ofmembership functions comprises storing membership function datarepresenting a characteristic relationship between a variable (signallevel change or previous tracking adjustment) and its degree ofsatisfaction, said membership function data being common to pluralmembership functions in said set, and storing position data identifyinga respective position of each of said plural membership functions insaid set.
 3. The method of claim 2 wherein said variable is normalized,and wherein said position data represents coordinates along an abscissaat which the respective membership functions in said set begin.
 4. Themethod of claim 1 wherein said step of inferring tracking controlcomprises providing a third set of tracking control membership functionsrepresenting degrees to which tracking control values satisfypredetermined ranges of values, selecting from the third set at leastone tracking control membership function in response to the membershipfunctions determined from said first and second sets and in accordancewith predetermined reasoning rules, and deriving the tracking controlfrom the selected tracking control membership function.
 5. The method ofclaim 4 wherein the derived tracking control represents the trackingcontrol direction value; and further comprising the steps of providingan additional set of membership functions representing respectivedegrees to which the detected signal level satisfies predeterminedranges of signal levels; selecting at least one membership function fromsaid additional set corresponding to said detected signal level; andusing specific reasoning rules to infer the tracking control magnitudevalue from the membership functions selected from said additional setand from the derived tracking control direction value.
 6. The method ofclaim 5 wherein the step of using specific reasoning rules to infer thetracking control magnitude value includes selecting at least onetracking control membership function from said third set in accordancewith said specific reasoning rules, and modifying a last-mentionedselected tracking control membership function in response to a lesser ofthe membership function selected from said additional set and thederived tracking control direction value.
 7. The method of claim 6wherein said step of adjusting the tracking of said head in response tosaid tracking control data comprises determining a substantial center ofgravity of the modified tracking control membership function, andgenerating an adjustment signal in response to the determined center ofgravity.
 8. A method of controlling a tracking of a head relative to amedium from which signals are played back comprising the steps of:detecting a signal level of signals which are played back; generatingtracking control data as a function of the detected signal level byproviding first (ΔE), second (E(n)) and third (CX1(n-1)) sets ofmembership functions respectively representing a degree to which achange in the detected signal level (ΔE), the degree to which the levelof the detected signal (E(n)) and the degree to which a precedingtracking adjustment (CX1(n-1)) satisfy predetermined ranges of values,selecting at least one membership function from said first, second andthird sets in response to a determined change in the detected signallevel and the level of the detected signal and in accordance withspecific reasoning rules, determining a center of gravity of the atleast one membership function selected from said third set, andgenerating a tracking control signal in response to the determinedcenter of gravity; and adjusting the tracking of said head in responseto said tracking control data.
 9. The method of claim 8 wherein saidpreceding tracking adjustment (CX1(n-1)) represents a direction andmagnitude of tracking adjustment; and wherein said step of selecting atleast one membership function from said first, second and third setsincludes selecting those membership functions from said first set (ΔE)which are satisfied by the degree of change in the detected signal level(ΔE), selecting those membership functions from said third set(CX1(n-1)) which are satisfied by the degree of a preceding trackingadjustment (CX1(n-1)), pairing the membership functions selected fromsaid first set with the membership functions selected from said thirdset in accordance with said specific reasoning rules, limiting a valueof a larger one of paired membership functions with the degree ofsatisfaction exhibited by a smaller one of the paired membershipfunctions, and combining the limited membership functions in all pairsto produce an inferred tracking control direction characteristic. 10.The method of claim 9 wherein said step of selecting at least onemembership function from said first, second and third sets furtherincludes selecting those membership functions from said second set(E(n)) which are satisfied by the level of the detected signal (E(n)),selecting those membership functions from said third set (CX1(n-1)) inresponse to the membership functions selected from said second set andthe inferred tracking control direction pursuant to said specificreasoning rules, and selectively limiting the values of the membershipfunctions selected from said third set as a function of the degree ofsatisfaction exhibited by the membership function selected from saidsecond set or the degree of inferred tracking control direction. 11.Apparatus for controlling a tracking of a head relative to a medium fromwhich signals are played back comprising level detecting means fordetecting a signal level of signals which are played back; fuzzy controlmeans responsive to the detected signal level for generating presenttracking control direction and magnitude values to adjust the trackingof the head, said fuzzy control means comprising memory means forstoring a first set of membership functions representing respectivedegrees to which changes in the detected signal level satisfypredetermined ranges of change and a second set of membership functionsrepresenting respective degrees to which previous tracking controldirection and magnitude adjustments satisfy predetermined ranges ofadjustment, and processor means programmed to retrieve from said memorymeans membership functions from said first and second sets correspondingto a detected signal level change and to a preceding tracking controldirection and magnitude adjustment, and to infer said present trackingcontrol direction and magnitude values from the retrieved membershipfunctions; and adjustment means for adjusting the tracking of said headin response to the present tracking control value.
 12. The apparatus ofclaim 11 wherein said memory means stores membership function datarepresenting a characteristic relationship between a variable (signallevel change or previous tracking adjustment) and its degree ofsatisfaction, said membership function data being common to pluralmembership functions in said set, and position data identifying arespective position of each of said plural membership functions in saidset.
 13. The apparatus of claim 12 wherein said variable is normalized,and wherein said position data represents coordinates along an abscissaat which the respective membership functions in said set begin.
 14. Theapparatus of claim 11 wherein said memory means stores a third set oftracking control membership functions representing degrees to whichtracking control values satisfy predetermined ranges of values; andwherein said processor means is further programmed to retrieve from saidmemory means at least one tracking control membership function from thethird set in response to the membership functions retrieved from saidfirst and second sets and in accordance with predetermined reasoningrules, and to derive the tracking control from the tracking controlmembership function retrieved from said third set.
 15. The apparatus ofclaim 14 wherein the derived tracking control represents the trackingcontrol direction value; wherein said memory means stores an additionalset of membership functions representing respective degrees to which thedetected signal level satisfies predetermined ranges of signal levels;and wherein said processor means is additionally programmed to retrievefrom said memory means at least one additional set corresponding to saiddetected signal level, and to use specific reasoning rules to infer thetracking control magnitude value from the membership functions retrievedfrom said additional set and from the derived tracing control directionvalue.
 16. The apparatus of claim 15 wherein said processor means isprogrammed to use specific reasoning rules to infer the tracking controlmagnitude value by retrieving from said memory means at least onetracking control membership function from said third set in accordancewith said specific reasoning rules, and to modify a last-mentionedretrieved tracking control membership function in response to a lesserof the membership function retrieved from the additional set and thederived tracking control direction value.
 17. The apparatus of claim 16wherein said adjustment means includes means for determining asubstantial center of gravity of the modified tracking controlmembership function, and means for generating an adjustment signal inresponse to the determining means.
 18. Apparatus for controlling atracking of a playback head relative to a medium from which signals areplayed back comprising: level detecting means for detecting a signallevel of signals which are played back; fuzzy control means responsiveto the detected signal level for generating tracking control data toadjust the tracking of the head, said fuzzy control means comprisingmemory means for storing first (ΔE), second (E(n)) and third (CX1(n-1))sets of membership functions respectively representing a degree to whicha change in the detected signal level (ΔE), the degree to which thelevel of the detected signal (E(n)) and the degree to which a precedingtracking adjustment (CX1(n-1)) satisfy predetermined ranges of values,and processor means programmed to select at least one membershipfunction from said first, second and third sets as a function of adetermined change in the detected signal level and the level of thedetected signal, and in accordance with specific reasoning rules, todetermine a center of gravity of at least one membership functionselected from said third set, and to generate a tracking control signalin response to the determined center of gravity; and adjustment meansfor adjusting the tracking of said head in response to said trackingcontrol data.
 19. The apparatus of claim 18 wherein said precedingtracking adjustment (CX1(n-1)) represents a direction and magnitude oftracking adjustment; and wherein said processor means is furtherprogrammed to select those membership functions from said first set (ΔE)which are satisfied by the degree of change in the detected signal level(ΔE), to select those membership functions from said third set(CX1(n-1)) which are satisfied by the degree of preceding trackingadjustment. (CX1(n-1)), to pair the membership functions selected fromsaid first set with the membership functions selected from said thirdset in accordance with said specific reasoning rules, to limit a valueof a larger one of the paired membership functions with the degree ofsatisfaction exhibited by a smaller of the paired membership functions,and to combine the limited membership functions in all pairs to producean inferred tracking control direction characteristic.
 20. The apparatusof claim 19 wherein said processor means is additionally programmed toselect those membership functions from said second set (E(n)) which aresatisfied by the level of the detected signal (E(n)), to select thosemembership functions from said third set (CX1(n-1)) in response to themembership functions selected from said second set and the inferredtracking control direction pursuant to said specific reasoning rules,and to selectively limit the values of the membership functions selectedfrom said third set as a function of the degree of satisfactionexhibited by the membership function selected form said second set orthe degree of inferred tracking control direction.